Abstract
An (m, n, 2)-balanced Latin rectangle is an \({m \times n}\) array on symbols 0 and 1 such that each symbol occurs n times in each row and m times in each column, with each cell containing either two 0’s, two 1’s or both 0 and 1. We completely determine the structure of all critical sets of the full (m, n, 2)-balanced Latin rectangle (which contains 0 and 1 in each cell). If m, \({n \geq 2}\), the minimum size for such a structure is shown to be \({(m-1)(n-1)+1}\). Such critical sets in turn determine defining sets for (0, 1)-matrices.
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Cavenagh, N., Raass, V. Critical Sets of 2-Balanced Latin Rectangles. Ann. Comb. 20, 525–538 (2016). https://doi.org/10.1007/s00026-016-0322-0
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DOI: https://doi.org/10.1007/s00026-016-0322-0